An outstanding defensive performance was the foundation on which Steve Clarke's team recorded its second win of the season to continue its unbeaten run in the Premier League
Long, who had hit the bar in the first half, converted Peter Odemwingie's low cross from the left to put the Baggies ahead.
The points were sealed when McAuley, who played a big part in an outstanding defensive performance by Steve Clarke's team, then beat Tim Howard to a corner in the latter stages to end the Toffees' 100 percent start to the campaign.
Neither side included any new signings made in the final days of the transfer window in their squads, with Everton completing a deal for the versatile Copenhagen player Bryan Oviedo too late for him to feature.
West Brom was missing the bench threat of Romelu Lukaku, but were able to include Odemwingie, who had also been an injury doubt, among their substitutes.
Everton exerted most of the early pressure, with the powerful duo of Marouane Fellaini and Nikica Jelavic pinning back the West Brom defense. Ben Foster remained untested, however, despite the crosses aimed into the box and referee Jon Moss rightly waved played on when Jelavic appealed for a penalty under the challenge of Claudio Yacob.
It was West Brom who eventually had the first real chance of the contest having grown into their passing game as the half hour mark approached. Shortly after Graham Dorrans' through ball had just escaped James Morrison, Long rattled the crossbar with a header from Liam Ridgewell's excellent cross.
The substitution of Darron Gibson, who suffered an injury, was a factor in the deterioration of Everton's performance and control of possession in the first half but even when they did reach the penalty area, West Brom center backs McAuley and Jonas Olsson competed strongly with Fellaini and Jelavic and permitted headed attempts only from unthreatening areas.
Their defensive solidity was nearly rewarded when Morrison found space in the center of the pitch to advance at goal, rounding Sylvain Distin on the way, but Tim Howard made an excellent save to deny the Scottish midfielder.
Everton continued to edge the possession stakes in the second half and finally created a chance of note when substitute Kevin Mirallas rolled in a cross from the right that Fellaini clumsily blazed over the crossbar with his left foot when unmarked at the back post.
West Brom had introduced a wide forward of its own from the bench in Odemwingie, and the Nigerian created the first goal of the same in much the same way as Mirallas had laid on that gilt-edged chance for Everton. Escaping the attention of Hibbert down the left, he fired a low cross into the box that evaded Phil Jagielka and was tapped in by Long from close range.
Victor Anichebe was added to the Everton attack as Moyes attempted to find a spark of inspiration but McAuley, Olsson and company held firm.
Indeed, it was West Brom who looked more likely to exploit the space left by Everton's raids forward, with Yacob and Mulumbu going close from distance.
And when the latter's shot was palmed behind by Howard, McAuley stole in front of the goalkeeper from the resulting corner to seal the points and continue the Baggies' superb start to the season.
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